# D9.C.5 Member Capacities

Member design and code checking per AIJ 2002 are based upon the allowable stress design method. It is a method for proportioning structural members using design loads and forces, allowable stresses, and design limitations for the appropriate material under service conditions. The basic measure of member capacities are the allowable stresses on the member under various conditions of applied loading such as allowable tensile stress, allowable compressive stress etc. These depend on several factors such as cross sectional properties, slenderness factors, unsupported width to thickness ratios and so on. Explained here is the procedure adopted in STAAD for calculating such capacities.

## D9.C.5.1 Design Capabilities

All types of available shapes such as H-Shape, I-Shape, L-Shapes, channel, pipe, tube, etc. can be used as member property and STAAD.Pro will automatically adopt the design procedure for that particular shape if Steel Design is requested. The steel tables available within STAAD.Pro or user provided table (UPTABLE) can be used for member properties.

## D9.C.5.2 Methodology

For steel design, STAAD.Pro compares the actual stresses with the allowable stresses as required by AIJ specifications. The design procedure consist of following three steps.

1. Calculation of sectional properties

The program extracts section properties cross sectional area, A, the moment of inertia about Y and Z axes, Iyy and Izz, and the St. Venant torsional constant, J, from the built-in steel tables. The program then calculates the elastic section moduli, Zz and Zy, torsional section modulus, Zx, and radii of gyration, iy and iz, using the appropriate formulas.

For I shapes, H shapes, and channel sections, the program calculates the radius of gyration needed for bending using following formula:

$i = I i / A i$
2. Calculation of actual and allowable stresses

Allowable stresses for structural steel under permanent loading shall be determined on the basis of the values of F given in the following table.

Table 1. Table: Values of F (N/mm2)
Steel for Construction Structures Steel for General Structures Steel for Welded Structures
Thickness SN400

SNR400

STKN400

SN490

SNR490

STKN490

SS400

STK400

STKR400

SSC400

SWH400

SS490 SS540 SM400

SMA400

SM490

SM490 Y

SMA490

STKR490

STK490

SM520 SM570
t≤ 40 235 325 235 275 375 235 325 355 400
40< t ≤ 100 215 295 215 255 - 215 295* 335 400

* F = 325 N/mm2 when t > 75mm

Note: In checking members for temporary loading be the combination of stresses described in Chap.3, allowable stresses specified in this chapter may be increases by 50%

Program calculates actual and allowable stresses by following methods:

1. Axial Stress:

Actual tensile stresses,

 FT = force / ( A × NSF )

where
 NSF = Net Section Factor for tension input as a design parameter

Actual compressive stress , FC = force / A

Allowable tensile stress, ft

• = FYLD / 1.5 (For Permanent Case)
• = FYLD ( For Temporary Case )
where
 FYLD = Yield stress input as a design parameter

Allowable compressive stress, fc

 $f c = { [ 1 − 0.4 ( λ Λ ) 2 ] F ν when λ ⁢ ≤ Λ 0.277 F ( λ Λ ) 2 when λ ⁢ > Λ$

 = fc × 1.5 (for Temporary case)

where
 Λ = $π 2 E 0.6 F$ ν = $3 2 + 2 3 ( λ Λ ) 2$

Actual torsional stress, ft = torsion / Zx

where
 Zx = J / max(tf, tw) tf = flange thickness tw = web thickness
2. Bending Stress:

Actual bending stress for My for compression

 ( Fbcy) = My / Zcy

Actual bending stress for Mz for compression

 ( Fbcz) = Mz / Zcz

Actual bending stress for My for tension

 ( Fbty ) = My / Zty

Actual bending stress for Mz for tension

 ( Fbtz ) = Mz / Ztz

where
 Zcy, Zcz = elastic section modulus for compression due to bending about the y and z axes, respectively Zty, Ztz = elastic section modulus for tension due to bending about the y and z axes, respectively
Note: The web is ignored in the calculation of Zz for H-shape, I-shape, and channel sections when the MBG parameter = 1.

Allowable bending stress for My

(fbcy) = ft

Allowable bending stress for Mz

 (fbcz) = { 1 - .4 x (lb / i)2 / (C λ2)} ft max

 = 89,000/ (lb × h / Af )

For Temporary case, fbcz = 1.5 x (fbcz for Permanent case)

where
 C = 1.75 - 1.05 (M2 / M1) + 0.3 (M2 / M1)2
• Allowable bending stress for My, fbty = ft
• Allowable bending stress for Mz, fbtz = fbcz
Note: The parameter CB can be used to specify a value for C directly.
3. Shear Stress

Actual shear stresses are calculated by the following formula:

 qy = Qy / Aww

where
 Aww = web shear area = product of depth and web thickness

 qz = Qz / Aff

where
 Aff = flange shear area = 2/3 times total flange area fs = Allowable shear stress, Fs / 1.5, Fs = F / √(3)
3. Checking design requirements:

User provided RATIO value (default 1.0) is used for checking design requirements

The following conditions are checked to meet the AIJ specifications. For all the conditions calculated value should not be more than the value of RATIO. If for any condition value exceeds RATIO, the program gives the message that the section fails.

Conditions:

1. Axial tensile stress ratio = FT / ft
2. Axial compressive stress ratio = FC / fc
3. Combined compression & bending compressive ratio = FC / fc+Fbcz/fbcz+Fbcy/fbcy
4. Combined compression & bending tensile ratio = (Fbtz+Fbty-FC) / ft
5. Combined tension & bending tensile ratio = (FT+Fbtz+Fbty) / ft
6. Combined tension & bending compressive ratio = Fbcz/fbcz+Fbcy/fbcy- FT/ft
7. Shear stress ratio in Y = qy / fs
8. Shear stress ratio in Z = qz / fs
9. von Mises stress ratio (if the von Mises stresses were set to be checked) = fm/(k⋅ft)

## D9.C.5.4 Allowable stress for Axial Tension

Allowable axial stress in tension is calculated per section 5.1 (1) of the AIJ code. In members with axial tension, the tensile load must not exceed the tension capacity of the member. The tension capacity of the member is calculated on the basis of the member area. STAAD calculates the tension capacity of a given member based on a user supplied net section factor (NSF-a default value of 1.0 is present but may be altered by changing the input value, see Table 8B.1) and proceeds with member selection or code checking.

## D9.C.5.5 Allowable stress for Axial Compression

The allowable stress for members in compression is determined according to the procedure of section 5.1 (3). Compressive resistance is a function of the slenderness of the cross-section (Kl/r ratio) and the user may control the slenderness value by modifying parameters such as KY, LY, KZ and LZ. In the absence of user provided values for effective length, the actual member length will be used. The slenderness ratios are checked against the permissible values specified in Chapter 11 of the AIJ code.

## D9.C.5.6 Allowable stress for Bending

The permissible bending compressive and tensile stresses are dependent on such factors as length of outstanding legs, thickness of flanges, unsupported length of the compression flange (UNL, defaults to member length) etc.  The allowable stresses in bending (compressive and tensile) are calculated as per the criteria of Clause 5.1 (4) of the code.

## D9.C.5.7 Allowable stress for Shear

Shear capacities are a function of web depth, web thickness etc. The allowable stresses in shear are computed according to Clause 5.1 (2) of the code.